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Advanced Methods of Structural Analysis Igor A. Karnovsky Olga Lebed (cid:129) Advanced Methods of Structural Analysis 123 IgorA.Karnovsky OlgaLebed 811NorthviewPl. CondorRebarConsultants,Inc. CoquitlamBCV3J3R4 300-1128HornbySt. Canada VancouverBCV6Z2L4 Canada ISBN978-1-4419-1046-2 e-ISBN978-1-4419-1047-9 DOI10.1007/978-1-4419-1047-9 SpringerNewYorkDordrechtHeidelbergLondon LibraryofCongressControlNumber:2009936795 (cid:2)c SpringerScience+BusinessMedia,LLC2010 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Dedicatedto TamaraL’vovna Gorodetsky Preface Theoryoftheengineeringstructuresisafundamentalscience.Statementsandmeth- odsofthissciencearewidelyusedindifferentfieldsofengineering.Amongthem are thecivilengineering,ship-building,aircraft,robotics,space structures,as well asnumerousstructuresofspecialtypesandpurposes–bridges,towers,etc.Inrecent years,evenmicromechanicaldevicesbecomeobjectsofstructuralanalysis. Theory of the engineering structures is alive and is a very vigorous science. This theory offers an engineer-designer a vast collection of classical methods of analysisofvarioustypesofstructures.Thesemethodscontainin-depthfundamen- tal ideas and, at the presenttime, they are developedwith sufficient completeness and commonness,aligned in a well-composedsystem of conceptions,procedures, and algorithms, use modern mathematical techniques and are brought to elegant simplicityandperfection. We now live in a computerized world. A role and influence of modern engineering software for analysis of structures cannot be overestimated. The modern computer programs allow providing different types of analysis for any sophisti- catedstructure.Asthistakesplace,whatistheroleofclassicaltheoryofstructures withitsin-depthideas,prominentconceptions,methods,theorems,andprinciples? Knowing classical methods of Structural Analysis is necessary for any practical engineer.Anengineercannotrelyonlyontheresultsprovidedbyacomputer.Com- puter is a great help in modeling differentsituations and speeding up the process of calculations, but it is the sole responsibility of an engineerto check the results obtainedbyacomputer.Ifusersofcomputerengineeringsoftwaredonothavesuf- ficient knowledge of fundamentals of structural analysis and of understanding of physical theories and principal properties of structures, then he/she cannot check obtainednumericalresultsandtheircorrespondencetoanadopteddesigndiagram, aswellasexplainresultsobtainedbyacomputer.Computerprograms“...canmake a good engineer better, but it can make a poor engineer more dangerous” (Cook R.D, MalkusD.S, Plesha M.E (1989)Concepts and applicationsof finite element analysis, 3rd edn. Wiley, New York). Only the knowledge of fundamental theory of structuresallows to estimate and analyze numericaldata obtainedfrom a computer;predictthe behaviorof a structure as a result of changinga design diagram and parameters; design a structure which satisfies certain requirements; perform serious scientific analysis; and make valid theoretical generalizations. No matter vii viii Preface how sophisticated the structural model is, no matter how effective the numerical algorithms are, no matter how powerful the computers are that implement these algorithms,it is the engineerwho analyzesthe endresult producedfromthese algorithms.Onlyanindividualwhohasa deepknowledgeandunderstandingofthe structuralmodelandanalysistechniquescanproduceaqualitativeanalysis. In1970,oneoftheauthorsofthisbookwasaprofessoratastructuralengineer- ing university in Ukraine. At that time computerswere started to be implemented in all fields of science, structural analysis being one of them. We, the professors andinstructors,werefacingaseriousmethodicaldilemma:giventhenewtechnolo- gies,howtoproperlyteachthestudents?Wouldwefirstgivestudentsastrongbasis in classical structural analysis and then introducethem to the related software, or would we directly dive into the software after giving the student a relatively in- significantintroductiontoclassicalanalysis.Wedidnotknowtheoptimalwayfor solvingthisproblem.Onthissubjectwehaveconductedseminarsanddiscussions onaregularbasis.Wehaveusedthesetwomainteachingmodels,andmanydiffer- entvariationsofthem.Theresultwassomewhatsurprising.Thestudentswhowere firstgivenastrongfoundationinstructuralanalysisquicklylearnedhowtousethe computersoftware,andwereabletogiveagoodqualitativeanalysisoftheresults. Thestudentswhoweregivenabriefintroductiontostructuralanalysisandastrong emphasisonthecomputersoftware,attheendwerenotabletoprovidequalitative results of the analysis. The interesting thing is that the students themselves were criticizingthelaterteachingstrategy. Therefore, our vision of teaching structural analysis is as follows: on the first step, it is necessary to learn analytical methods, perform detailed analysis of different structures by hand in order to feel the behavior of structures, and correlate their behavior with obtained results; the second step is a computer application of engineeringsoftware. Authorswrotethebookonthebasisoftheirmanyyearsofexperienceofteaching theStructuralAnalysisattheuniversitiesforgraduateandpostgraduatestudentsas wellasonthebasisoftheirexperienceinconsultingcompanies. This book is written for students of universities and colleges pursuing Civil or StructuralEngineeringPrograms,instructorsofStructuralAnalysis,andengineers anddesignersofdifferentstructuresofmodernengineering. Theobjectiveofthebookistohelpareadertodevelopanunderstandingofthe ideasandmethodsofstructuralanalysisandtoteachareadertoestimateandexplain numericalresults obtainedby hand;this is a fundamentalstone for preparationof readerfornumericalanalysisofstructuresandforuseofengineeringsoftwarewith fullunderstanding. ThetextbookoffersthereaderthefundamentaltheoreticalconceptsofStructural Analysis,classicalanalyticalmethods,algorithmsoftheirapplication,comparison ofdifferentmethods,andavastcollectionofdistinctiveproblemswiththeirdetailed solution, explanation, analysis, and discussion of results; many of the problems haveacomplexcharacter.Consideredexamplesdemonstratefeaturesofstructures, theirbehavior,andpeculiaritiesofappliedmethods.Solutionofalltheproblemsis broughttofinalformulaornumber. Preface ix Analyses of the following structures are considered: statically determinate and indeterminate multispan beams, arches, trusses, and frames. These structures are subjectedtofixedandmovingloads,changesoftemperature,settlementofsupports, anderrorsoffabrication.Alsothecablesareconsideredindetail. In many cases, same structure under different external actions is analyzed. It allows the readerto be concentratedon one designdiagramand performcomplex analysisofbehaviorofastructure. Inmanycases,samestructureisanalyzedbydifferentmethodsorbyonemethod in different forms (for example, Displacement method in canonical, and matrix forms). It allows to perform comparison analysis of applied methods and see ad- vantagesanddisadvantagesofdifferentmethods. DistributionofMaterial inthe Book Thisbookcontainsintroduction,threeparts(14chapters),andappendix. IntroductionprovidesthesubjectandpurposesofStructuralAnalysis,principal concepts,assumptions,andfundamentalapproaches. Part 1 (Chaps. 1–6) is devoted to analysis of statically determinate structures. Among them are multispan beams, arches, trusses, cables, and frames. Construc- tion of influence lines and their application are discussed with great details. Also thispartcontainsanalyticalmethodsofcomputationofdisplacementofdeformable structures,subjectedtodifferentactions.Amongthemarevarietyloads,changeof temperature,andsettlementsofsupports. Part2(Chaps.7–11)isfocusedonanalysisofstaticallyindeterminatestructures usingthefundamentalmethods.Amongthemaretheforceanddisplacementmeth- ods(bothmethodsarepresentedincanonicalform),aswellasthemixedmethod. Alsotheinfluencelinemethod(onthebasisofforceanddisplacementmethods)is presented.Analysisofcontinuousbeams,arches,trusses,andframesisconsidered indetail. Chapter11 is devotedto matrix stiffnessmethodwhich is realized in the modern engineering software. Usually, the physical meaning of all matrix procedures presentsseriousdifficultiesforstudents. Comparisonofnumericalproceduresob- tainedby canonicalequationsand theirmatrix presentations,whichare appliedto the same structure, allows trace and understandsmeaning of each stage of matrix analysis.Thismethodisappliedforfixedloads,settlementofsupports,temperature changes,andconstructionofinfluencelines. Part3(Chaps.12–14)containsthreeimportanttopicsofstructuralanalysis.They areplasticbehaviorofstructures,stabilityofelasticstructureswithfiniteandinfinite numberofdegreesoffreedom,includinganalysisof structuresonthe basisofthe deformabledesigndiagram(P–(cid:2)analysis),andthefreevibrationanalysis. Each chapter contains problems for self-study. Answers are presented to all problems.